J Austral Math Soc Ser A 47 pp263--268, 1989.

The Volumes of Simplices, or, Find the Penguin

Fima C. Klebaner, Aidan Sudbury and G. A. Watterson

(Received 2 February 1988)

Abstract

Given the equations for the n + 1 hyperplanes that bound an n-simplex in Rⁿ, simple formulae are derived for the contents of the n - r simplices (0 Ł r < n) embedded in it. For example, when n = 3, the formulae include the volume of the tetrahedron, the areas of its faces and the lengths of its edges.

1980 AMS Subject Classification (1985 Revision): 14N99

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Authors

Fima C. Klebaner
Aidan Sudbury
G. A. Watterson: Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.

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Last Modified: Wed Feb 19 10:27:50 2003